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How do you use the chain rule to differentiate #y=root3(4x-1)#?

Answer 1

Emma Aldridge

#y'=4/(3root(3)((4x-1)^2))#

#y'=1/(3root(3)((4x-1)^2))*4=4/(3root(3)((4x-1)^2))#

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Answer 2

Axel Alvarez

To differentiate ( y = \sqrt{3}(4x - 1) ) using the chain rule, follow these steps:

Identify the outer function and the inner function.
- Outer function: ( \sqrt{3}u )
- Inner function: ( u = 4x - 1 )
Compute the derivative of the outer function with respect to its variable.
- ( \frac{d}{du}(\sqrt{3}u) = \sqrt{3} )
Compute the derivative of the inner function with respect to its variable.
- ( \frac{du}{dx} = 4 )
Apply the chain rule, multiplying the derivatives obtained in steps 2 and 3.
- ( \frac{dy}{dx} = \frac{d}{dx}(\sqrt{3}(4x - 1)) = \sqrt{3} \times 4 = 4\sqrt{3} )

So, the derivative of ( y = \sqrt{3}(4x - 1) ) is ( \frac{dy}{dx} = 4\sqrt{3} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.